Article Contents
Article Contents

# A symmetric property in the enhanced common index jump theorem with applications to the closed geodesic problem

• * Corresponding author: Wei Wang

The second author is supported by NSFC grant 12025101, 11431001

• In this paper, we prove a symmetric property for the indices for symplectic paths in the enhanced common index jump theorem (cf. Theorem 3.5 in [6]). As an application of this property, we prove that on every compact Finsler manifold $(M, \, F)$ with reversibility $\lambda$ and flag curvature $K$ satisfying $\left(\frac{\lambda}{\lambda+1}\right)^2<K\le 1$, there exist two elliptic closed geodesics whose linearized Poincaré map has an eigenvalue of the form $e^{\sqrt {-1}\theta}$ with $\frac{\theta}{\pi}\notin{\bf Q}$ provided the number of closed geodesics on $M$ is finite.

Mathematics Subject Classification: Primary: 53C22, 53C60; Secondary: 58E10.

 Citation:

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